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plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
import os
import numpy as np
import scipy.io
from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix, mean_squared_error, r2_score
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from IPython.display import clear_output
import random
import sys
After reading and preprocessing the data in the next code chunk, the data from all cells is stored in a population dictionary. The dictionary's keys correspond to the cell names, and the values contain the data for each respective cell.
The values in the population dictionary are cell dictionaries with keys being 'axons', 'green_dFFMeanValues',and 'red_dFFMeanValues':
'axons', e.g., cell_data_dict['CL090_230515']['axons'] is a 1 dimensional numpy array, of which the length is the number of groups and the elements are 1 dimensional numpy arrays consisting of components belonging to the group.'green_dFFMeanValues' is a 2 dimensional 3 by 49 numpy array (each cell has 3 rounds, and each round has 8 directions * 2 time frequencies * 3 space frequencies = 48 settings plus a extra period so in total there are 49 columns), of which the elements are still 2 dimensional numpy arrays with size being 10 by N (N is the number of components).'red_dFFMeanValues' is similarly a 2 dimensional 3 by 49 numpy array, of which the elements are still 2 dimensional numpy arrays with size being 10 by 1 (only recording the data at the soma).root_path = "/content/drive/MyDrive/Fluorescence_Data/FluoData4Fitting_Average"
# Get a list of all the subdirectories: subfolders are viewed as cell names
cell_names = [f for f in os.listdir(root_path) if os.path.isdir(os.path.join(root_path, f))]
# for cell in cell_names:
# print(cell)
# Create a dictionary with default values
default_value = 0
cell_data_dict = {cell: default_value for cell in cell_names}
# print(cell_data_dict)
file_suffixes = ['green_Axon.mat', 'green_dFFMeanValues.mat', 'red_dFFMeanValues.mat']
for cell in cell_names:
print(cell)
file_names = [cell + suffix for suffix in file_suffixes]
path_ = file_names[0] # green_Axon.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
axons = mat_data['Axons'] # array containing nested arrays/sub-arrays
# Squeeze the outer array
axons = np.squeeze(axons, axis=0)
for i in range(len(axons)):
# Squeeze the inner array and convert the data type to 'int'
axons[i] = np.squeeze(axons[i].astype(int), axis=0)
# final axons' length is the number of groups with
# each elements being a nested array of components
path_ = file_names[1] # green_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_green = mat_data['dFFMeanValues'] # 3 by 49
path_ = file_names[2] # red_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_red = mat_data['dFFMeanValues'] # 3 by 49
cell_data_dict[cell] = {'axons': axons,
'green_dFFMeanValues': dFFMeanValues_green,
'red_dFFMeanValues': dFFMeanValues_red}
# Print keys and types
for key, value in cell_data_dict.items():
print("-- * * * * * --")
print(key, type(value))
for key_, value_ in value.items():
print(key_, type(value_))
print("-- * * * * * --")
CL090_230515 CL090_230518 CL083_230413 CL075_230303 -- * * * * * -- CL090_230515 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL090_230518 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL083_230413 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL075_230303 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * --
# print to see data type and size
print(cell_data_dict['CL090_230515'].keys())
print(type(cell_data_dict['CL090_230515']['axons']))
print(cell_data_dict['CL090_230515']['axons'].shape)
print(cell_data_dict['CL090_230515']['axons'][1].shape)
print(cell_data_dict['CL090_230515']['axons'][1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].dtype)
dict_keys(['axons', 'green_dFFMeanValues', 'red_dFFMeanValues']) <class 'numpy.ndarray'> (25,) (19,) int64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 281) (10, 155) float64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 1) (10, 2) float64
Note:
Four cells: 'CL090_230515', 'CL090_230518', 'CL083_230413', 'CL075_230303'.
'red_dFFMeanValues' and 'green_dFFMeanValues' have 49 columns,where the last column should be excluded. They are supposed to have 3 rows (3 rounds), but 'CL090_230518' only has 2 rows.
In 'CL083_230413', elements in 'red_dFFMeanValues' have 2 columns (10 × 2， should be 10 × 1), so 'CL083_230413' is not used.
def plot_comparison(y_test, y_pred, subtitle = ''):
# Sort y_pred and y_test based on y_test
sorted_indices = np.argsort(y_test)
sorted_y_pred = y_pred[sorted_indices]
sorted_y_test = y_test[sorted_indices]
# Plot sorted_y_pred and sorted_y_test
plt.plot(sorted_y_pred, label='Sorted Predictions')
plt.plot(sorted_y_test, label='Sorted Ground Truth')
plt.xlabel('Index')
plt.ylabel('Value')
plt.title(f'Comparison of Sorted Predictions and Sorted Ground Truth \n ({subtitle})')
plt.legend()
plt.savefig(f'Comparison of Sorted Predictions and Sorted Ground Truth ({subtitle}).png', bbox_inches='tight')
# bbox_inches='tight' will adjust the figure's bounding box to fit all the content, ensuring that
# the complete words are visible in the saved figure. Otherwise, the saved figure may not show the
# complete words, e.g., for x-label, or for the long title.
# The default setting can sometimes result in cutoff or clipped text. It tries to include the entire
# figure within the saved image, but there may be cases where the default behavior is not sufficient
# to capture all the content. The default behavior assumes the figure content fits within the predefined
# margins and padding.
plt.show()
cell_data = cell_data_dict['CL090_230515']
data_green = cell_data['green_dFFMeanValues'][:,:-1] # exclude 49th column
data_red = cell_data['red_dFFMeanValues'][:,:-1] # exclude 49th column
data_axons = cell_data['axons']
# vstack green data
stacked_green = np.empty((0, data_green[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_green):
stacked_green = np.vstack((stacked_green, value))
print(stacked_green.shape, 48*3*10)
# group columns of green data
group_num = data_axons.shape[0]
group_satcked_green = np.zeros((stacked_green.shape[0], group_num))
for i, cols in enumerate(data_axons):
group_satcked_green[:, i] = np.sum(stacked_green[:, cols-1], axis=1)
print(group_satcked_green.shape, data_axons.shape)
# vstack red data
stacked_red = np.empty((0, data_red[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_red):
stacked_red = np.vstack((stacked_red, value))
print(stacked_red.shape, 48*3*10)
print(np.max(group_satcked_green), np.min(group_satcked_green))
print(np.max(stacked_red), np.min(stacked_red))
(1440, 281) 1440 (1440, 25) (25,) (1440, 1) 1440 15.553237533160676 -5.301797778486449 0.6745208147710272 -0.24153973313562027
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,)
Ordinary least squares Linear Regression.
Linear Regression fits a linear model with coefficients to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
# Create a LinearRegression object
model = linear_model.LinearRegression()
# Fit the model on the training data
model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Predict on the test data
y_pred = model.predict(x_test)
Fitted Coefficients: [ 8.28301566e-03 7.56874223e-03 2.17645374e-04 -2.06269935e-03 3.53903502e-03 5.16754189e-03 1.24691680e-03 2.32002780e-02 2.40241470e-03 -6.16858257e-03 -1.20710729e-03 2.78029746e-02 9.57603350e-03 -4.35972960e-03 3.04637298e-03 6.77257749e-03 8.29508492e-04 3.04802829e-02 -6.67335217e-04 9.61650591e-03 -2.47112388e-02 -1.14696165e-03 8.29246943e-02 -1.13145597e-02 -3.19379843e-01] Fitted Intercept: -0.003966473464240797
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.007927335708322457 Correlation coefficient: 0.6140976886111208 Coefficient of determination (R-squared score, R2 score): 0.3610848833977214
plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.0061596970599993445 Correlation coefficient: 0.6571303587882936 Coefficient of determination (R-squared score, R2 score): 0.43182030844123154
plot_comparison(y_train, y_pred_, 'Ordinary Linear Regression, Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.486111111111111 Correlation coefficient: 0.6292717941149766 Coefficient of determination (R-squared score, R2 score): 0.36944077498899164 Mean squared error: 2.0255847953216373 Correlation coefficient: 0.6340286499988343 Coefficient of determination (R-squared score, R2 score): 0.4011018872884826
Linear least squares with l2 regularization.
Minimizes the objective function:
$$ ||y - Xw||^2_2 + \alpha ||w||^2_2 $$This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm.
# Create a Ridge Regression object
ridge_model = linear_model.Ridge(alpha=1.0) # You can adjust the value of alpha as per your requirements
# Fit the model on the training data
ridge_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", ridge_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", ridge_model.intercept_)
# Predict on the test data
y_pred = ridge_model.predict(x_test)
Fitted Coefficients: [ 0.00849453 0.00740115 0.00016157 -0.0020944 0.0034469 0.00444959 0.00196809 0.0228857 0.0024516 -0.00571464 -0.00091334 0.0277737 0.00929144 -0.00475298 0.00350069 0.00617136 -0.00020173 0.02975458 -0.00172438 0.01062452 -0.02926797 -0.00329156 0.01071774 -0.01549336 -0.06836985] Fitted Intercept: -0.003992042396819981
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Ridge Linear Regression, Test Set')
Mean squared error: 0.008058648873285792 Correlation coefficient: 0.6047541953182045 Coefficient of determination (R-squared score, R2 score): 0.35050150845424777
# predict on train
# Use the trained model to make predictions
y_pred_ = ridge_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Ridge Linear Regression, Train Set')
Mean squared error: 0.00617267529320373 Correlation coefficient: 0.6562194390940245 Coefficient of determination (R-squared score, R2 score): 0.43062317675322503
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.486111111111111 Correlation coefficient: 0.6290805964856068 Coefficient of determination (R-squared score, R2 score): 0.36944077498899164 Mean squared error: 2.038011695906433 Correlation coefficient: 0.6311655529544047 Coefficient of determination (R-squared score, R2 score): 0.3974276657381052
Linear regression with combined L1 and L2 priors as regularizer.
Minimizes the objective function:
$$ 1 / (2 * n_{samples}) * ||y - Xw||^2_2 + \alpha * l1_{ratio} * ||w||_1 + 0.5 * \alpha * (1 - l1_{ratio}) * ||w||^2_2 $$If controlling the L1 and L2 penalty separately, that this is equivalent to:
$$ a * ||w||_1 + 0.5 * b * ||w||_2^2 $$where: $\alpha = a + b$ and $l1_{ratio} = a / (a + b)$.
# Create an ElasticNet object
a = 0.004; b = 0.00
alpha = a + b; l1_ratio = a / (a + b)
elasticnet_model = linear_model.ElasticNet(alpha=alpha, l1_ratio=l1_ratio, max_iter=100000)
# adjust the values of alpha and l1_ratio as per your requirements
# Fit the model on the training data
elasticnet_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", elasticnet_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", elasticnet_model.intercept_)
# Predict on the test data
y_pred = elasticnet_model.predict(x_test)
# It is normal to encounter warning here, because our data is not linear enough
# and not normailized to guarantee a low error/residual, even though we set a very
# large max_iter. But the results is similar to that of ordinary and Ridge linear
# regression. Like alpha = 0 results in the same results as the ordinary linear
# rergession.
Fitted Coefficients: [ 0.00951724 0.0068485 0. -0. 0.00285676 0. 0. 0.01545406 0.00635406 -0. 0. 0.02601547 0.00529342 -0. 0. 0.00326147 0. 0. 0. 0. -0. 0. 0. -0. -0. ] Fitted Intercept: -0.004587622786060119
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Elasticnet Linear Regression, Test Set')
Mean squared error: 0.008246618904776503 Correlation coefficient: 0.593481482809575 Coefficient of determination (R-squared score, R2 score): 0.33535179119658987
# predict on train
# Use the trained model to make predictions
y_pred_ = elasticnet_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Elasticnet Linear Regression, Train Set')
Mean squared error: 0.006385274236585692 Correlation coefficient: 0.6428087118878939 Coefficient of determination (R-squared score, R2 score): 0.4110127314829676
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 2.7777777777777777 Correlation coefficient: 0.566099913342907 Coefficient of determination (R-squared score, R2 score): 0.2954645530603258 Mean squared error: 2.1052631578947367 Correlation coefficient: 0.6144590454550366 Coefficient of determination (R-squared score, R2 score): 0.3775436432301804
Mathematically, a power-law relationship can be expressed as:
$$ y = A X^C $$Here, I modify it, shown as:
$$ y = A (X+B)^C + D $$where, $X = \beta_1 x_1 + \beta_2 x_2 \dots + \beta_N x_N$. $X+D$ is a linear regression part. $A$, $B$, $C$, $D$, $\beta_1$, $\beta_2$, ...,$\beta_N$ are parameters to be determined.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,)
exponent = 5
# Define the model function
def func(X, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
base = weighted_sum + B
power_result = np.power(base, exponent)
return A * power_result + D
# Create a LinearRegression object
model = linear_model.LinearRegression()
# give the initial params using linear regression
# so that the params are within a reasonable range
model.fit(x_train, y_train)
# print("Fitted Coefficients:", model.coef_)
# print("Fitted Intercept:", model.intercept_)
num_features = x_train.shape[1]
# Assuming model.coef_ is the np array containing the coefficients
model_coefs = model.coef_
# Set negative elements to 0 using np.clip()
initial_params = [1, model.intercept_, 0] + list(model_coefs) # Initial parameter guesses
# model_coefs_clipped = np.clip(model_coefs, 0, np.inf)
# initial_params = [1, model.intercept_, 0] + list(model_coefs_clipped) # Initial parameter guesses, no need to clip -- they can be negative
# Set lower and upper bounds for the parameters
lower_bounds = [0, -np.inf, -np.inf] + [0] * num_features
upper_bounds = [np.inf, np.inf, np.inf] + [np.inf] * num_features
# Combine the lower and upper bounds into a 2-tuple of array_like
bounds = (lower_bounds, upper_bounds)
# Perform the curve fit with bounds
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, bounds=bounds, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, B, D = params[:3]
weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred = A * sign * power_result + D
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression (Exponent=5), Test Set')
# predict on train
A, B, D = params[:3]
weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred_ = A * sign * power_result + D
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression (Exponent=5), Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 3.63589934e+00 5.17800351e-01 -1.38641935e-01 4.83492282e-03 4.37660663e-03 -3.27563273e-04 -1.65395632e-05 2.76270197e-03 3.60564181e-03 1.18571822e-03 1.39874639e-02 9.74478013e-04 -4.33905140e-03 3.12368809e-04 1.63689641e-02 5.70510078e-03 -3.84107281e-03 9.86178700e-04 3.44528993e-03 1.88010948e-04 1.79227711e-02 -6.87188789e-03 6.36542080e-03 -1.91319680e-02 -5.91287026e-04 3.77753461e-02 -1.06618770e-02 -1.74782336e-01] Mean squared error: 0.007801938801087381 Correlation coefficient: 0.6219617870348478 Coefficient of determination (R-squared score, R2 score): 0.3711914289705994
Mean squared error: 0.005965096684632098 Correlation coefficient: 0.6706493415945699 Coefficient of determination (R-squared score, R2 score): 0.44977053881398854
---- ---- ---- Mean squared error: 2.611111111111111 Correlation coefficient: 0.6064419746929176 Coefficient of determination (R-squared score, R2 score): 0.3377366798767063 Mean squared error: 1.939327485380117 Correlation coefficient: 0.653816054551323 Coefficient of determination (R-squared score, R2 score): 0.42660530746169045
# compared with example 1, here only fit A and D.
exponent = 5
model = linear_model.LinearRegression()
model.fit(x_train, y_train)
# now we have: model.intercept_ and model.coef_
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Define the model function
def func(X, A, D):
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(model.coef_), axis=1)
base = weighted_sum
power_result = np.power(base, exponent)
return A * power_result + D
initial_params = [1, 0]
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, D = params
y_pred = func(x_test, A, D)
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, only fit A and D, Test Set')
# predict on train
A, D = params
y_pred_ = func(x_train, A, D)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression Exponent=5, only fit A and D, Train Set')
Fitted Coefficients: [ 8.28301566e-03 7.56874223e-03 2.17645374e-04 -2.06269935e-03 3.53903502e-03 5.16754189e-03 1.24691680e-03 2.32002780e-02 2.40241470e-03 -6.16858257e-03 -1.20710729e-03 2.78029746e-02 9.57603350e-03 -4.35972960e-03 3.04637298e-03 6.77257749e-03 8.29508492e-04 3.04802829e-02 -6.67335217e-04 9.61650591e-03 -2.47112388e-02 -1.14696165e-03 8.29246943e-02 -1.13145597e-02 -3.19379843e-01] Fitted Intercept: -0.003966473464240797 Fitted Parameters: [3.06877195e+02 3.73110121e-02] Mean squared error: 0.010403693780630378 Correlation coefficient: 0.4740522878239656 Coefficient of determination (R-squared score, R2 score): 0.16149921366803333
Mean squared error: 0.00901247587500699 Correlation coefficient: 0.41070148964947206 Coefficient of determination (R-squared score, R2 score): 0.16867571360029543
# generate irreducible fraction with an odd number as the denominator
# such numbers can work as the exponent for negative numbers and
# will be used as the parameter "C" in Power-law regression below:
# y = A * (B+b1*x1+b2*x2+...+bN*xN)**C + D
def gcd(a, b): # calculate the greatest common divisor of two numbers
while b:
a, b = b, a % b
return a
def generate_irreducible_fraction(existing_fractions = []):
while True:
numerator = random.randint(1, 400) # Random numerator
denominator = random.randrange(1, 100, 2) # Random odd denominator
if gcd(numerator, denominator) == 1: # Check if the fraction is irreducible
fraction = (numerator, denominator)
if fraction not in existing_fractions: # Check if the fraction is not a duplicate
return fraction
# Generate irreducible fraction numbers
N_faction = 40
upper_bound = 50
irreducible_fractions = []
while len(irreducible_fractions) < N_faction:
fraction = generate_irreducible_fraction(irreducible_fractions)
if fraction[0]/fraction[1] < upper_bound:
irreducible_fractions.append(fraction)
# Sort the irreducible fractions
irreducible_fractions.sort(key=lambda f: f[0] / f[1])
# Print the irreducible fraction numbers
for numerator, denominator in irreducible_fractions:
if random.random() <= 0.1:
print(f"{numerator}/{denominator}")
# Extract the numerator and denominator values
indexes = range(1, len(irreducible_fractions) + 1)
values = [numerator / denominator for numerator, denominator in irreducible_fractions]
# Plot the irreducible fractions
plt.plot(values, 'o-')
plt.xlabel("Index")
plt.ylabel("Irreducible Fraction")
plt.title("Irreducible Fractions")
plt.show()
## if not use the above random generated irreducible_fractions, define it below.
irreducible_fractions = [(1,95), (30,43), (179,65), (5,1), (221,33), (219,23), (300,17), (73,3)]
3/11 60/83 382/19
# # old code! The new one is in the next chunk.
# params_list = []
# for numerator, denominator in irreducible_fractions:
# C1, C2 = numerator, denominator
# # Define the model function
# def func(X, *params):
# A, B, D = params[:3]
# # Compute the weighted sum
# weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# return A * sign * power_result + D
# # Create a LinearRegression object
# model = linear_model.LinearRegression()
# # give the initial params using linear regression
# # so that the params are within a reasonable range
# model.fit(x_train, y_train)
# # print("Fitted Coefficients:", model.coef_)
# # print("Fitted Intercept:", model.intercept_)
# num_features = x_train.shape[1]
# initial_params = [1, model.intercept_, 0] + list(model.coef_) # Initial parameter guesses
# # Perform the curve fit
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params_list.append(params)
# # Print the fitted parameters
# # print("Fitted Parameters:", params)
# # predict on test
# y_predict_test_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred = A * sign * power_result + D
# y_predict_test_list.append(y_pred)
# # predict on train
# y_predict_train_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred_ = A * sign * power_result + D
# y_predict_train_list.append(y_pred_)
# new code, a updated version for the code in last chunk.
# input and output data normalization is achieved (but it
# seems normalization is redundant).
class CurveFit_with_Normalization:
def __init__(self, exponent_numerator=1, exponent_denominator=1, input_range=[1,2], output_range=[1,2]):
self.input_min = input_range[0]
self.input_max = input_range[1]
self.output_min = output_range[0]
self.output_max = output_range[1]
self.input_scale = None
self.input_shift = None
self.output_scale = None
self.output_shift = None
self.exponent_numerator = exponent_numerator
self.exponent_denominator = exponent_denominator
self.linear_model = linear_model.LinearRegression()
def fit(self, X, y):
# Normalize the input and output data
self.input_scale = (self.input_max - self.input_min) / (np.max(X) - np.min(X))
self.input_shift = self.input_min - np.min(X) * self.input_scale
normalized_X = self.input_scale * X + self.input_shift
self.output_scale = (self.output_max - self.output_min) / (np.max(y) - np.min(y))
self.output_shift = self.output_min - np.min(y) * self.output_scale
normalized_y = self.output_scale * y + self.output_shift
def normalized_func_(X_normalize, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, self.exponent_numerator / self.exponent_denominator)
return A * sign * power_result + D
# Give the initial params using linear regression
self.linear_model.fit(normalized_X, normalized_y)
# print("Fitted Coefficients:", linear_model.coef_)
# print("Fitted Intercept:", linear_model.intercept_)
# num_features = X.shape[1]
exponent = self.exponent_numerator / self.exponent_denominator
initial_params = [1, self.linear_model.intercept_ / exponent + (1 - 1 / exponent), 0] + list(self.linear_model.coef_ /
exponent) # Initial parameter guesses
# initial_params = [1, 0, 0] + [1 / X.shape[1]] * (X.shape[1])
# Perform the normalized curve fit
normalized_params, params_covariance = curve_fit(normalized_func_, normalized_X, normalized_y,
p0=initial_params, maxfev=100000000)
# Store the fitted parameters
self.normalized_fitted_params = normalized_params
def predict(self, X):
# Normalize the input data using the previously calculated scaling and shifting parameters
normalized_X = self.input_scale * X + self.input_shift
# Make predictions using the denormalized parameters
y_pred = self.normalized_func(normalized_X, self.exponent_numerator,
self.exponent_denominator, *self.normalized_fitted_params)
# Denormalize the predicted output
y_pred = (y_pred - self.output_shift) / self.output_scale
return y_pred
@staticmethod
def normalized_func(X_normalize, exponent_numerator, exponent_denominator, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent_numerator / exponent_denominator)
return A * sign * power_result + D
model_list = []
for numerator, denominator in irreducible_fractions:
# Create an instance of NormalizedCurveFit
model = CurveFit_with_Normalization(numerator, denominator, input_range=[1, 2], output_range=[1, 2])
# Fit the model to your input and output data
model.fit(x_train, y_train)
model_list.append(model)
# this is for the new version code in the last chunk
r2_score_test_list = []
# predict on test
y_predict_test_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred = model.predict(x_test)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_test_list.append(r_squared)
y_predict_test_list.append(y_pred)
print("|||||||||||||||||||||||||||||||||||||")
r2_score_train_list = []
# predict on train
y_predict_train_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred_ = model.predict(x_train)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
y_predict_train_list.append(y_pred_)
x = [numerator / denominator for (numerator, denominator) in irreducible_fractions]
# plot the r2 score curve over exponent
fig, ax = plt.subplots(figsize=(7.5, 5)) # Adjust the values as desired
# Plot the R-squared scores
ax.plot(x, r2_score_train_list, label='Train R-squared')
ax.plot(x, r2_score_test_list, label='Test R-squared')
# Set labels and title with font size
ax.set_xlabel('Exponent in Power Law', fontsize=14)
ax.set_ylabel('R-squared', fontsize=14)
ax.set_title('R-squared Scores', fontsize=16)
# Set tick label font size
ax.tick_params(axis='x', labelsize=12)
ax.tick_params(axis='y', labelsize=12)
# Set legend
ax.legend(fontsize=12)
fig.savefig('Power_Law_r2_scores_plot.png')
# Display the plot
plt.show()
-------- (numerator, denominator) is: (1, 95) Mean squared error: 0.012553698090272793 Correlation coefficient: 0.5492586362659945 Coefficient of determination (R-squared score, R2 score): -0.01178350132389605 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.007927645253546677 Correlation coefficient: 0.6140764914279518 Coefficient of determination (R-squared score, R2 score): 0.36105993515151313 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.0077922987749738555 Correlation coefficient: 0.6224739461963064 Coefficient of determination (R-squared score, R2 score): 0.3719683808539297 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.007801721831719279 Correlation coefficient: 0.6219708360133526 Coefficient of determination (R-squared score, R2 score): 0.37120891593144234 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.007804194315316004 Correlation coefficient: 0.6218374974348415 Coefficient of determination (R-squared score, R2 score): 0.37100964253069046 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.00780588812404452 Correlation coefficient: 0.6217442394863175 Coefficient of determination (R-squared score, R2 score): 0.37087312756007484 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.007807965450587863 Correlation coefficient: 0.6216287490698504 Coefficient of determination (R-squared score, R2 score): 0.37070570241504563 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.007809033771437306 Correlation coefficient: 0.6215582319310625 Coefficient of determination (R-squared score, R2 score): 0.37061959954704493 ||||||||||||||||||||||||||||||||||||| -------- (numerator, denominator) is: (1, 95) Mean squared error: 0.01045316636333401 Correlation coefficient: 0.4156817350556336 Coefficient of determination (R-squared score, R2 score): 0.03578426304422133 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.006160312058280804 Correlation coefficient: 0.6570871953391387 Coefficient of determination (R-squared score, R2 score): 0.43176358007773163 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.0059664793888465975 Correlation coefficient: 0.6705542454661818 Coefficient of determination (R-squared score, R2 score): 0.4496429961042646 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.005965096687271862 Correlation coefficient: 0.6706493409961944 Coefficient of determination (R-squared score, R2 score): 0.44977053857049276 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.0059651110041034 Correlation coefficient: 0.6706483564323005 Coefficient of determination (R-squared score, R2 score): 0.44976921796448766 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.005965205069629524 Correlation coefficient: 0.6706418874831295 Coefficient of determination (R-squared score, R2 score): 0.44976054121933307 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.00596536777619391 Correlation coefficient: 0.6706306978729792 Coefficient of determination (R-squared score, R2 score): 0.449745532921901 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.005965431990408115 Correlation coefficient: 0.6706262817005308 Coefficient of determination (R-squared score, R2 score): 0.4497396097065115
# for model in model_list:
# print(model.exponent_numerator, model.exponent_denominator)
# both the old and new versions (in the last subsection "Fit and predict") of code
# share the same evaluate code in this subsectoon.
# Create and update multiple figures (test)
for y_pred, (numerator, denominator) in zip(y_predict_test_list, irreducible_fractions):
plot_comparison(y_test, y_pred, f'Power-Law Regression Exponent={numerator} over {denominator}, Test Set')
# here pay attention: cannot use / replace over in the name, otherwise cannot save the fig
# because / cannot be in a file name.
print(y_pred[0])
clear_output(wait=True) # Clear the previous output
0.024177814296192267
# Create and update multiple figures (train)
for y_pred_, (numerator, denominator) in zip(y_predict_train_list, irreducible_fractions):
plot_comparison(y_train, y_pred_, f'Power-Law Regression Exponent={numerator} over {denominator}, Train Set')
print(y_pred_[0])
clear_output(wait=True) # Clear the previous output
0.08987348912424292
Let $B = (b_1, b_2, \ldots , b_N)$. $$ y = A \cdot e^{(b_1 \cdot x_1 + \ldots + b_N \cdot x_N)} + C $$
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,)
# Define the model function
def func(X, *params):
A, C = params[:2]
return A * np.exp(np.sum(X * np.array(params[2:]), axis=1)) + C
# give the initial params using linear regression
# so that the params are within a reasonable range
num_features = x_train.shape[1]
initial_params = [np.mean(y_train), 0] + [0] * num_features # Initial parameter guesses
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, C = params[:2]
y_pred = A * np.exp(np.sum(x_test * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# predict on train
A, C = params[:2]
y_pred_ = A * np.exp(np.sum(x_train * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 1.87123029e-01 -1.90080285e-01 3.40033178e-02 3.05772821e-02 -2.49194815e-03 4.85530544e-05 1.95783707e-02 2.48969634e-02 8.90102191e-03 9.83075781e-02 6.65559330e-03 -3.03907795e-02 1.30905974e-03 1.15904357e-01 4.00205951e-02 -2.72080362e-02 6.22504795e-03 2.48130071e-02 3.73831850e-04 1.26144436e-01 -4.97544159e-02 4.56011391e-02 -1.34034892e-01 -3.74403443e-03 2.63216376e-01 -7.38379867e-02 -1.21397447e+00] Mean squared error: 0.007809965919858963 Correlation coefficient: 0.6215183575736783 Coefficient of determination (R-squared score, R2 score): 0.3705444716933213 Mean squared error: 0.005965612679987845 Correlation coefficient: 0.6706138550826338 Coefficient of determination (R-squared score, R2 score): 0.44972294262878365 ---- ---- ---- [ 0.02425583 0.14706718 0.12366429 0.0786443 0.04049227 0.23597745 -0.01620631 0.13441449 0.07236053 0.21618206 -0.01070742 0.06076135 -0.0189932 0.02788252 -0.0500517 -0.01343889 -0.05818453 0.11900008 0.09522372 0.00959078 0.03787487 0.13463547 0.0192085 0.05924506 0.01095437 0.06465591 0.08565256 0.02403056 0.0302071 0.10111491 -0.03160033 -0.01100594 0.16379375 -0.00697092 0.05063293 -0.03982638 0.29517585 0.00586459 0.05913923 -0.01925285 -0.03112963 0.05716643 0.0669799 0.05498539 0.01261709 -0.01698296 0.16587962 0.20025347 0.02612595 0.01466163 0.04731695 0.03795217 0.03130737 0.08110612 0.01362295 0.09130886 0.04140823 -0.08651457 0.18025977 -0.03097426 -0.01282914 0.02221508 0.02125931 -0.00187638 0.10262163 -0.01400319 -0.01616673 0.11696926 0.04167538 -0.00686065 0.08243136 0.059111 ] [4 6 6 5 4 8 3 6 5 7 4 5 3 4 3 3 3 6 5 4 4 6 4 5 4 5 5 4 4 5 3 4 7 4 5 3 9 4 5 3 3 5 5 5 4 3 7 7 4 4 5 4 4 5 4 5 4 2 7 3 3 4 4 4 6 3 3 6 4 4 5 5] Mean squared error: 2.6527777777777777 Correlation coefficient: 0.5985681611539189 Coefficient of determination (R-squared score, R2 score): 0.32716864817261115 Mean squared error: 1.9305555555555556 Correlation coefficient: 0.6558085630583136 Coefficient of determination (R-squared score, R2 score): 0.4291988756148981
plot_comparison(y_test, y_pred, 'Exponential Regression, Test Set')
plot_comparison(y_train, y_pred_, 'Exponential Regression, Train Set')
# independent data
x = group_satcked_green
class_num = 480
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,) Unique elements: [ 0 7 27 36 38 40 43 50 52 54 55 56 57 58 60 61 62 63 65 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 210 211 212 213 214 215 216 217 218 219 220 222 223 224 226 227 228 229 230 231 232 233 234 235 237 238 240 242 243 244 245 246 247 250 251 253 254 255 256 257 258 259 260 263 265 266 267 268 269 270 272 273 274 277 280 283 285 286 287 288 290 291 293 294 300 310 311 315 322 323 326 327 329 332 334 335 336 339 340 343 349 356 357 360 369 380 383 389 391 426 475 479] Number of unique elements: 253
'multinomial' (default option for multi-calss) achieves better performance than 'ovr'.
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
# model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='ovr')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
print("Coefficients:", model.coef_[0,:])
print("Intercept:", model.intercept_[0])
print('--- --- ---')
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
print('y_prob.shape:', y_prob.shape)
print(np.sum(y_prob, axis = 1))
print(y_prob[0,:])
# Print the predicted class labels
print('y_pred:', y_pred)
print('y_test:', y_test)
print('y_pred shape:', y_pred.shape, 'y_test shape:', y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(253,) (253, 25) Coefficients: [-0.56105226 -0.62859538 -0.46179994 -0.6925927 -0.30706826 -0.01190705 -0.45737944 -0.17699687 -0.62488952 0.51399664 -0.34089166 -0.34399414 0.27368915 -0.11936503 -0.22297636 0.02269972 -0.35553952 -0.40214045 -0.00632174 -0.31621744 -0.016341 0.06506962 -0.07248956 -0.05043361 -0.02148207] Intercept: -0.8575836013108327 --- --- --- y_prob.shape: (72, 253) [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [3.00513727e-06 1.78744497e-05 4.74271558e-06 2.26308841e-06 4.53582848e-04 2.95953122e-04 3.82431244e-04 6.93949432e-04 5.98212044e-04 4.66303629e-03 4.76670086e-06 1.50275557e-03 9.30465729e-03 4.59748348e-05 1.23666672e-05 3.81004232e-06 5.58735220e-07 4.89590297e-05 1.94336182e-03 2.18697241e-05 1.18488676e-04 2.35866565e-04 8.48631165e-04 9.48281252e-05 4.13887514e-04 4.22881901e-04 7.18182737e-05 8.54745095e-04 4.27335681e-04 1.29495961e-03 2.94954570e-04 5.47908929e-03 4.90149592e-04 8.71618141e-04 9.76115172e-05 4.23398791e-03 2.57026839e-04 4.12272636e-04 5.72641661e-05 4.95932025e-04 4.97701787e-03 6.89949821e-03 1.67311130e-04 8.00211126e-03 1.29303602e-03 2.03940831e-03 2.90252042e-04 8.60263501e-04 1.25532128e-02 1.96396600e-03 2.94995906e-03 2.29869096e-03 2.52056220e-03 2.54046320e-03 3.61508754e-03 6.41644563e-04 1.87148723e-03 4.89574558e-03 5.02775497e-03 3.27392327e-02 2.38527541e-02 2.46410302e-03 3.10847814e-03 1.21985752e-03 2.46154288e-02 1.01599575e-02 6.83543333e-03 2.66300071e-02 7.98466521e-03 1.13087216e-03 1.29043331e-02 2.38046011e-02 7.47311391e-04 1.78326785e-02 6.14558292e-02 4.54307674e-03 6.00180238e-03 3.50709096e-03 1.88260156e-02 2.28465105e-02 5.53181977e-03 1.14844449e-02 3.04061894e-03 5.59138033e-02 2.47701263e-02 2.53208946e-02 4.48656516e-02 6.83942450e-03 7.49985832e-03 1.06915049e-02 1.36389724e-02 4.66767982e-03 8.07249715e-03 5.11675482e-03 2.06943731e-03 5.82958060e-03 5.76255114e-03 4.58914148e-03 4.66574638e-04 2.48459793e-03 3.03024389e-02 1.14737057e-02 1.48355678e-03 8.96805350e-03 4.27718262e-03 2.55261125e-02 6.87853119e-03 6.73633047e-03 2.78849055e-03 1.48657664e-03 9.20821197e-03 1.48883412e-03 5.71632058e-03 2.69526177e-03 1.25210487e-02 1.70457261e-02 5.40348402e-03 7.54221885e-03 3.17343122e-03 4.04628878e-03 1.59134015e-03 3.38044325e-03 1.17740638e-02 2.06243969e-02 7.68512392e-03 1.65720427e-03 1.67597704e-03 7.47441136e-04 9.40485225e-03 8.09834810e-04 3.09079655e-04 4.60063811e-03 3.60651458e-04 2.01370207e-03 9.16105334e-05 1.01061821e-03 1.53768067e-02 1.78599908e-03 1.89423123e-03 3.66742299e-04 1.80925433e-04 5.71428042e-04 4.47115486e-03 6.57157329e-03 2.31219664e-03 1.35079367e-03 2.74038945e-04 3.83427767e-03 3.90998872e-03 4.96950620e-04 1.15381962e-03 5.20356131e-05 4.88319433e-05 5.54816585e-04 1.30305277e-03 1.43730614e-03 3.72037874e-04 2.74543329e-04 2.15903026e-03 1.57887188e-03 1.70177036e-03 1.72214331e-03 9.47859292e-05 1.02799712e-04 7.27857561e-07 1.70807550e-04 1.70738087e-04 2.66587945e-04 3.15831384e-04 7.13953839e-04 2.21621458e-04 4.10680136e-03 1.05631355e-04 4.27200006e-05 2.97115519e-03 1.61543879e-05 5.09689647e-03 1.05839674e-04 8.75555582e-06 2.42098071e-06 8.42593081e-04 9.57099524e-04 3.75626604e-05 3.12464106e-04 5.86684109e-06 2.38019419e-06 3.54418016e-04 1.41452320e-07 1.89816390e-04 1.82709282e-03 1.59873894e-03 1.32139610e-06 9.82859548e-05 4.05675495e-06 3.13274180e-06 4.61319716e-04 1.41501606e-06 5.31509642e-05 3.93780310e-05 9.95147588e-04 2.58805822e-03 6.14909947e-06 2.78893982e-04 2.96500232e-04 1.62679259e-05 4.35621408e-06 5.95755878e-04 4.45307065e-04 4.42199814e-04 1.65588637e-04 1.40511540e-04 1.25233039e-04 9.10654471e-06 6.53158492e-08 1.26363834e-02 3.57053876e-06 4.92587186e-07 6.58464290e-07 1.28392972e-05 3.16635650e-06 2.87248256e-05 2.20759364e-04 1.59761185e-05 4.88102647e-05 3.06700085e-05 2.31340711e-04 2.47036710e-04 1.75085773e-04 3.08114917e-05 5.16169235e-05 1.76352269e-04 1.28049604e-05 3.12686717e-06 4.18501672e-05 2.25692519e-06 7.24950771e-06 2.75336483e-05 2.66506514e-05 1.60810997e-04 5.04695259e-05 2.88458128e-05 1.87919281e-04 2.78863401e-05 8.48976500e-05 2.16008788e-05 1.85055177e-06 8.44840014e-06 5.90515843e-04 9.90753216e-05 2.30940303e-05 1.87307075e-04 6.89947046e-05 3.83568617e-06] y_pred: [122 168 182 158 129 293 132 244 223 291 122 161 110 108 132 84 78 138 211 145 131 199 116 129 130 184 163 137 165 153 141 126 188 113 148 75 327 166 131 117 108 134 120 124 132 141 184 211 196 127 130 138 97 144 134 129 126 103 183 145 123 135 145 106 162 145 119 171 138 122 184 170] y_test: [195 131 252 352 130 217 105 183 176 281 157 180 79 165 107 86 109 128 254 299 149 219 127 161 115 160 139 143 97 185 152 134 189 128 113 101 306 160 142 122 122 124 300 124 124 137 176 282 115 178 99 150 117 151 160 222 189 108 179 76 189 112 120 93 150 136 85 221 170 118 160 163] y_pred shape: (72,) y_test shape: (72,)
In previous data division, I classify data into class_num (e.g., class_num = 160) intervals (hitogram, by np.digitize). Here, evaluate the results with the same number of classes (e.g., class_num = 160).
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_test, y_pred)
print("Confusion Matrix:") # y_test doesn't include all classes, so confusion matrix is less than num_class by num_class
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# Sort y_pred and y_test based on y_test
plot_comparison(y_test, y_pred, 'Logistic Linear Regression, Test Set')
Accuracy: 0.013888888888888888 Confusion Matrix: [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 1 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] Mean squared error: 2563.9444444444443 Correlation coefficient: 0.5661491222250555 Coefficient of determination (R-squared score, R2 score): 0.24678329168154234
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_train, y_pred_)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression, Train Set')
Accuracy: 0.2361111111111111 Confusion Matrix: [[1 0 0 ... 0 0 0] [0 1 0 ... 0 0 0] [0 0 1 ... 0 0 0] ... [0 0 0 ... 1 0 0] [0 0 0 ... 0 1 0] [0 0 0 ... 0 0 1]] Mean squared error: 1427.1834795321638 Correlation coefficient: 0.7559823206669919 Coefficient of determination (R-squared score, R2 score): 0.5203541026650583
The model is based on classifying data into class_num (e.g., class_num = 160) intervals (hitogram, by np.digitize). Here, evaluate the results a samller number of classes (e.g., reduced_class_num = 16), that is, for the example of class_num = 160 and reduced_class_num = 16, classes 0, 1, ..., 15 become one class, i.e., 0; ...; classes 144, 145, ..., 159 become one class, i.e., 15.
print("---- ---- ----")
# Define the boundaries for digitization
reduced_class_num = 16
intervals = np.arange(0, class_num + 1, class_num / reduced_class_num)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] [122 168 182 158 129 293 132 244 223 291 122 161 110 108 132 84 78 138 211 145 131 199 116 129 130 184 163 137 165 153 141 126 188 113 148 75 327 166 131 117 108 134 120 124 132 141 184 211 196 127 130 138 97 144 134 129 126 103 183 145 123 135 145 106 162 145 119 171 138 122 184 170] [ 4 5 6 5 4 9 4 8 7 9 4 5 3 3 4 2 2 4 7 4 4 6 3 4 4 6 5 4 5 5 4 4 6 3 4 2 10 5 4 3 3 4 4 4 4 4 6 7 6 4 4 4 3 4 4 4 4 3 6 4 4 4 4 3 5 4 3 5 4 4 6 5] Mean squared error: 2.7222222222222223 Correlation coefficient: 0.6060794440849583 Coefficient of determination (R-squared score, R2 score): 0.3095552619991193 Mean squared error: 1.7105263157894737 Correlation coefficient: 0.7442081479296433 Coefficient of determination (R-squared score, R2 score): 0.49425421012452153
Fixing the reduced class number, I enumerate the original class number to see what a original class number is better.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
reduced_class_num = 16
class_num_array = np.arange(reduced_class_num, reduced_class_num * 100 + 1, reduced_class_num)
mse_test_list = []
correlation_test_list = []
r_squared_test_list = []
mse_train_list = []
correlation_train_list = []
r_squared_train_list = []
for class_num in class_num_array:
print('---- ---- ----')
print(f'class_num = {class_num}')
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
# print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
y_pred = model.predict(x_test)
y_pred_ = model.predict(x_train)
# Define the boundaries for digitization
intervals = np.arange(0, class_num+1, class_num/16)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
# print(y_pred)
# print(y_pred_test_digital)
print("test eval:")
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_test_list.append(mse)
correlation_test_list.append(correlation)
r_squared_test_list.append(r_squared)
print("train eval:")
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_train_list.append(mse)
correlation_train_list.append(correlation)
r_squared_train_list.append(r_squared)
plot_comparison(y_test, y_pred, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Test Set')
plot_comparison(y_train, y_pred_, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Train Set')
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,) ---- ---- ---- class_num = 16 Number of unique elements: 16 [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.] test eval: Mean squared error: 3.5972222222222223 Correlation coefficient: 0.47198973344177797 Coefficient of determination (R-squared score, R2 score): 0.08762659621312197 train eval: Mean squared error: 2.2989766081871346 Correlation coefficient: 0.5910190720855697 Coefficient of determination (R-squared score, R2 score): 0.32026901318017964
---- ---- ---- class_num = 32 Number of unique elements: 29 [ 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.] test eval: Mean squared error: 3.236111111111111 Correlation coefficient: 0.5357558077876284 Coefficient of determination (R-squared score, R2 score): 0.17921620431527963 train eval: Mean squared error: 2.2346491228070176 Correlation coefficient: 0.6136660388859967 Coefficient of determination (R-squared score, R2 score): 0.33928851297036855
---- ---- ---- class_num = 48 Number of unique elements: 40 [ 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4803971320092436 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 2.245614035087719 Correlation coefficient: 0.6144510013822345 Coefficient of determination (R-squared score, R2 score): 0.3360465527788591
---- ---- ---- class_num = 64 Number of unique elements: 54 [ 0. 4. 8. 12. 16. 20. 24. 28. 32. 36. 40. 44. 48. 52. 56. 60. 64.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.503739746255114 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 2.111111111111111 Correlation coefficient: 0.6485234829384348 Coefficient of determination (R-squared score, R2 score): 0.3758145977947087
---- ---- ---- class_num = 80 Number of unique elements: 64 [ 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. 60. 65. 70. 75. 80.] test eval: Mean squared error: 4.180555555555555 Correlation coefficient: 0.4427520028671864 Coefficient of determination (R-squared score, R2 score): -0.060325847644209674 train eval: Mean squared error: 2.215643274853801 Correlation coefficient: 0.6381027090493488 Coefficient of determination (R-squared score, R2 score): 0.3449079106356516
---- ---- ---- class_num = 96 Number of unique elements: 71 [ 0. 6. 12. 18. 24. 30. 36. 42. 48. 54. 60. 66. 72. 78. 84. 90. 96.] test eval: Mean squared error: 3.3472222222222223 Correlation coefficient: 0.504180754959501 Coefficient of determination (R-squared score, R2 score): 0.15103478643769264 train eval: Mean squared error: 2.1703216374269005 Correlation coefficient: 0.6520581653648752 Coefficient of determination (R-squared score, R2 score): 0.35830801276055746
---- ---- ---- class_num = 112 Number of unique elements: 84 [ 0. 7. 14. 21. 28. 35. 42. 49. 56. 63. 70. 77. 84. 91. 98. 105. 112.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.5037710872095293 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 2.1907894736842106 Correlation coefficient: 0.6513815613624006 Coefficient of determination (R-squared score, R2 score): 0.3522563537364065
---- ---- ---- class_num = 128 Number of unique elements: 94 [ 0. 8. 16. 24. 32. 40. 48. 56. 64. 72. 80. 88. 96. 104. 112. 120. 128.] test eval: Mean squared error: 3.375 Correlation coefficient: 0.5033317430794849 Coefficient of determination (R-squared score, R2 score): 0.14398943196829594 train eval: Mean squared error: 1.9546783625730995 Correlation coefficient: 0.6898003069787897 Coefficient of determination (R-squared score, R2 score): 0.42206656319357727
---- ---- ---- class_num = 144 Number of unique elements: 103 [ 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 90. 99. 108. 117. 126. 135. 144.] test eval: Mean squared error: 3.736111111111111 Correlation coefficient: 0.4735339459159608 Coefficient of determination (R-squared score, R2 score): 0.052399823866138284 train eval: Mean squared error: 2.0826023391812867 Correlation coefficient: 0.6695835615867002 Coefficient of determination (R-squared score, R2 score): 0.3842436942926333
---- ---- ---- class_num = 160 Number of unique elements: 112 [ 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.5242259606046868 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 2.1271929824561404 Correlation coefficient: 0.669450391726396 Coefficient of determination (R-squared score, R2 score): 0.3710597228471615
---- ---- ---- class_num = 176 Number of unique elements: 119 [ 0. 11. 22. 33. 44. 55. 66. 77. 88. 99. 110. 121. 132. 143. 154. 165. 176.] test eval: Mean squared error: 3.0555555555555554 Correlation coefficient: 0.5434058877638174 Coefficient of determination (R-squared score, R2 score): 0.22501100836635846 train eval: Mean squared error: 1.8801169590643274 Correlation coefficient: 0.7027983256653713 Coefficient of determination (R-squared score, R2 score): 0.4441118924958417
---- ---- ---- class_num = 192 Number of unique elements: 129 [ 0. 12. 24. 36. 48. 60. 72. 84. 96. 108. 120. 132. 144. 156. 168. 180. 192.] test eval: Mean squared error: 2.9722222222222223 Correlation coefficient: 0.5613286852055313 Coefficient of determination (R-squared score, R2 score): 0.24614707177454864 train eval: Mean squared error: 2.068713450292398 Correlation coefficient: 0.6795194596695697 Coefficient of determination (R-squared score, R2 score): 0.3883501772018787
---- ---- ---- class_num = 208 Number of unique elements: 135 [ 0. 13. 26. 39. 52. 65. 78. 91. 104. 117. 130. 143. 156. 169. 182. 195. 208.] test eval: Mean squared error: 3.263888888888889 Correlation coefficient: 0.5167605713638903 Coefficient of determination (R-squared score, R2 score): 0.17217084984588282 train eval: Mean squared error: 1.9714912280701755 Correlation coefficient: 0.6990042154331321 Coefficient of determination (R-squared score, R2 score): 0.417095557566596
---- ---- ---- class_num = 224 Number of unique elements: 144 [ 0. 14. 28. 42. 56. 70. 84. 98. 112. 126. 140. 154. 168. 182. 196. 210. 224.] test eval: Mean squared error: 3.2083333333333335 Correlation coefficient: 0.5437377502756681 Coefficient of determination (R-squared score, R2 score): 0.18626155878467632 train eval: Mean squared error: 2.017543859649123 Correlation coefficient: 0.6953029871474389 Coefficient of determination (R-squared score, R2 score): 0.40347932476225623
---- ---- ---- class_num = 240 Number of unique elements: 151 [ 0. 15. 30. 45. 60. 75. 90. 105. 120. 135. 150. 165. 180. 195. 210. 225. 240.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.5194551289734144 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 2.067982456140351 Correlation coefficient: 0.6873768774083306 Coefficient of determination (R-squared score, R2 score): 0.38856630788131263
---- ---- ---- class_num = 256 Number of unique elements: 162 [ 0. 16. 32. 48. 64. 80. 96. 112. 128. 144. 160. 176. 192. 208. 224. 240. 256.] test eval: Mean squared error: 3.361111111111111 Correlation coefficient: 0.5009248047595136 Coefficient of determination (R-squared score, R2 score): 0.1475121092029943 train eval: Mean squared error: 1.8940058479532165 Correlation coefficient: 0.7093807333281182 Coefficient of determination (R-squared score, R2 score): 0.4400054095865963
---- ---- ---- class_num = 272 Number of unique elements: 168 [ 0. 17. 34. 51. 68. 85. 102. 119. 136. 153. 170. 187. 204. 221. 238. 255. 272.] test eval: Mean squared error: 3.5277777777777777 Correlation coefficient: 0.48355826570450633 Coefficient of determination (R-squared score, R2 score): 0.1052399823866138 train eval: Mean squared error: 1.8157894736842106 Correlation coefficient: 0.728019282425673 Coefficient of determination (R-squared score, R2 score): 0.4631313922860306
---- ---- ---- class_num = 288 Number of unique elements: 174 [ 0. 18. 36. 54. 72. 90. 108. 126. 144. 162. 180. 198. 216. 234. 252. 270. 288.] test eval: Mean squared error: 3.5277777777777777 Correlation coefficient: 0.4899766682551543 Coefficient of determination (R-squared score, R2 score): 0.1052399823866138 train eval: Mean squared error: 2.021198830409357 Correlation coefficient: 0.6856906934944299 Coefficient of determination (R-squared score, R2 score): 0.40239867136508645
---- ---- ---- class_num = 304 Number of unique elements: 184 [ 0. 19. 38. 57. 76. 95. 114. 133. 152. 171. 190. 209. 228. 247. 266. 285. 304.] test eval: Mean squared error: 3.0694444444444446 Correlation coefficient: 0.545368270536066 Coefficient of determination (R-squared score, R2 score): 0.2214883311316601 train eval: Mean squared error: 1.9239766081871346 Correlation coefficient: 0.7049550788995437 Coefficient of determination (R-squared score, R2 score): 0.43114405172980375
---- ---- ---- class_num = 320 Number of unique elements: 191 [ 0. 20. 40. 60. 80. 100. 120. 140. 160. 180. 200. 220. 240. 260. 280. 300. 320.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.49449225822246445 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 2.08187134502924 Correlation coefficient: 0.6930186726826559 Coefficient of determination (R-squared score, R2 score): 0.3844598249720673
---- ---- ---- class_num = 336 Number of unique elements: 197 [ 0. 21. 42. 63. 84. 105. 126. 147. 168. 189. 210. 231. 252. 273. 294. 315. 336.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.44750228465446723 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.7997076023391814 Correlation coefficient: 0.7278634370384258 Coefficient of determination (R-squared score, R2 score): 0.46788626723357785
---- ---- ---- class_num = 352 Number of unique elements: 205 [ 0. 22. 44. 66. 88. 110. 132. 154. 176. 198. 220. 242. 264. 286. 308. 330. 352.] test eval: Mean squared error: 3.5694444444444446 Correlation coefficient: 0.48227115458952186 Coefficient of determination (R-squared score, R2 score): 0.09467195068251877 train eval: Mean squared error: 1.7675438596491229 Correlation coefficient: 0.7300415728003163 Coefficient of determination (R-squared score, R2 score): 0.4773960171286723
---- ---- ---- class_num = 368 Number of unique elements: 212 [ 0. 23. 46. 69. 92. 115. 138. 161. 184. 207. 230. 253. 276. 299. 322. 345. 368.] test eval: Mean squared error: 3.125 Correlation coefficient: 0.5332746426444116 Coefficient of determination (R-squared score, R2 score): 0.20739762219286662 train eval: Mean squared error: 1.9649122807017543 Correlation coefficient: 0.6962281852214511 Coefficient of determination (R-squared score, R2 score): 0.41904073368150174
---- ---- ---- class_num = 384 Number of unique elements: 219 [ 0. 24. 48. 72. 96. 120. 144. 168. 192. 216. 240. 264. 288. 312. 336. 360. 384.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.5059495216654009 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.641812865497076 Correlation coefficient: 0.7550314567695265 Coefficient of determination (R-squared score, R2 score): 0.5145704939913143
---- ---- ---- class_num = 400 Number of unique elements: 224 [ 0. 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 325. 350. 375. 400.] test eval: Mean squared error: 3.638888888888889 Correlation coefficient: 0.48420812404275726 Coefficient of determination (R-squared score, R2 score): 0.07705856450902682 train eval: Mean squared error: 1.601608187134503 Correlation coefficient: 0.757055265058668 Coefficient of determination (R-squared score, R2 score): 0.5264576813601825
---- ---- ---- class_num = 416 Number of unique elements: 226 [ 0. 26. 52. 78. 104. 130. 156. 182. 208. 234. 260. 286. 312. 338. 364. 390. 416.] test eval: Mean squared error: 3.388888888888889 Correlation coefficient: 0.4852968909152171 Coefficient of determination (R-squared score, R2 score): 0.1404667547335975 train eval: Mean squared error: 1.706140350877193 Correlation coefficient: 0.7477674868813875 Coefficient of determination (R-squared score, R2 score): 0.49555099420112536
---- ---- ---- class_num = 432 Number of unique elements: 234 [ 0. 27. 54. 81. 108. 135. 162. 189. 216. 243. 270. 297. 324. 351. 378. 405. 432.] test eval: Mean squared error: 3.6527777777777777 Correlation coefficient: 0.47036606231027916 Coefficient of determination (R-squared score, R2 score): 0.07353588727432847 train eval: Mean squared error: 1.861842105263158 Correlation coefficient: 0.7191920076627579 Coefficient of determination (R-squared score, R2 score): 0.44951515948169074
---- ---- ---- class_num = 448 Number of unique elements: 243 [ 0. 28. 56. 84. 112. 140. 168. 196. 224. 252. 280. 308. 336. 364. 392. 420. 448.] test eval: Mean squared error: 3.0833333333333335 Correlation coefficient: 0.5250607650409068 Coefficient of determination (R-squared score, R2 score): 0.21796565389696165 train eval: Mean squared error: 1.8011695906432748 Correlation coefficient: 0.7347557280791996 Coefficient of determination (R-squared score, R2 score): 0.46745400587470987
---- ---- ---- class_num = 464 Number of unique elements: 243 [ 0. 29. 58. 87. 116. 145. 174. 203. 232. 261. 290. 319. 348. 377. 406. 435. 464.] test eval: Mean squared error: 3.013888888888889 Correlation coefficient: 0.5562252199875786 Coefficient of determination (R-squared score, R2 score): 0.2355790400704535 train eval: Mean squared error: 1.712719298245614 Correlation coefficient: 0.7451863485220609 Coefficient of determination (R-squared score, R2 score): 0.4936058180862197
---- ---- ---- class_num = 480 Number of unique elements: 253 [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] test eval: Mean squared error: 2.7222222222222223 Correlation coefficient: 0.6060794440849583 Coefficient of determination (R-squared score, R2 score): 0.3095552619991193 train eval: Mean squared error: 1.7105263157894737 Correlation coefficient: 0.7442081479296433 Coefficient of determination (R-squared score, R2 score): 0.49425421012452153
---- ---- ---- class_num = 496 Number of unique elements: 257 [ 0. 31. 62. 93. 124. 155. 186. 217. 248. 279. 310. 341. 372. 403. 434. 465. 496.] test eval: Mean squared error: 3.5 Correlation coefficient: 0.4832186801513632 Coefficient of determination (R-squared score, R2 score): 0.11228533685601061 train eval: Mean squared error: 1.713450292397661 Correlation coefficient: 0.7396308046833006 Coefficient of determination (R-squared score, R2 score): 0.4933896874067857
---- ---- ---- class_num = 512 Number of unique elements: 265 [ 0. 32. 64. 96. 128. 160. 192. 224. 256. 288. 320. 352. 384. 416. 448. 480. 512.] test eval: Mean squared error: 3.4166666666666665 Correlation coefficient: 0.4900594619824944 Coefficient of determination (R-squared score, R2 score): 0.1334214002642008 train eval: Mean squared error: 1.631578947368421 Correlation coefficient: 0.755311210710647 Coefficient of determination (R-squared score, R2 score): 0.5175963235033898
---- ---- ---- class_num = 528 Number of unique elements: 270 [ 0. 33. 66. 99. 132. 165. 198. 231. 264. 297. 330. 363. 396. 429. 462. 495. 528.] test eval: Mean squared error: 4.027777777777778 Correlation coefficient: 0.43736758254217567 Coefficient of determination (R-squared score, R2 score): -0.021576398062527424 train eval: Mean squared error: 1.7470760233918128 Correlation coefficient: 0.7376111428489114 Coefficient of determination (R-squared score, R2 score): 0.48344767615282336
---- ---- ---- class_num = 544 Number of unique elements: 277 [ 0. 34. 68. 102. 136. 170. 204. 238. 272. 306. 340. 374. 408. 442. 476. 510. 544.] test eval: Mean squared error: 4.0 Correlation coefficient: 0.4100064508731889 Coefficient of determination (R-squared score, R2 score): -0.014531043593130732 train eval: Mean squared error: 1.5314327485380117 Correlation coefficient: 0.7705055211445285 Coefficient of determination (R-squared score, R2 score): 0.5472062265858431
---- ---- ---- class_num = 560 Number of unique elements: 277 [ 0. 35. 70. 105. 140. 175. 210. 245. 280. 315. 350. 385. 420. 455. 490. 525. 560.] test eval: Mean squared error: 3.9166666666666665 Correlation coefficient: 0.47230871755082143 Coefficient of determination (R-squared score, R2 score): 0.006605019815059454 train eval: Mean squared error: 1.6074561403508771 Correlation coefficient: 0.756754569333987 Coefficient of determination (R-squared score, R2 score): 0.5247286359247106
---- ---- ---- class_num = 576 Number of unique elements: 286 [ 0. 36. 72. 108. 144. 180. 216. 252. 288. 324. 360. 396. 432. 468. 504. 540. 576.] test eval: Mean squared error: 3.9722222222222223 Correlation coefficient: 0.42378310656099694 Coefficient of determination (R-squared score, R2 score): -0.007485689123734041 train eval: Mean squared error: 1.6564327485380117 Correlation coefficient: 0.7506155099667133 Coefficient of determination (R-squared score, R2 score): 0.510247880402635
---- ---- ---- class_num = 592 Number of unique elements: 292 [ 0. 37. 74. 111. 148. 185. 222. 259. 296. 333. 370. 407. 444. 481. 518. 555. 592.] test eval: Mean squared error: 3.388888888888889 Correlation coefficient: 0.49399417848482213 Coefficient of determination (R-squared score, R2 score): 0.1404667547335975 train eval: Mean squared error: 1.6542397660818713 Correlation coefficient: 0.7478476246087622 Coefficient of determination (R-squared score, R2 score): 0.5108962724409369
---- ---- ---- class_num = 608 Number of unique elements: 300 [ 0. 38. 76. 114. 152. 190. 228. 266. 304. 342. 380. 418. 456. 494. 532. 570. 608.] test eval: Mean squared error: 2.861111111111111 Correlation coefficient: 0.5654923211396736 Coefficient of determination (R-squared score, R2 score): 0.27432848965213563 train eval: Mean squared error: 1.5 Correlation coefficient: 0.7737523401399934 Coefficient of determination (R-squared score, R2 score): 0.5564998458015036
---- ---- ---- class_num = 624 Number of unique elements: 304 [ 0. 39. 78. 117. 156. 195. 234. 273. 312. 351. 390. 429. 468. 507. 546. 585. 624.] test eval: Mean squared error: 3.6666666666666665 Correlation coefficient: 0.41626635730762723 Coefficient of determination (R-squared score, R2 score): 0.07001321003963012 train eval: Mean squared error: 1.5402046783625731 Correlation coefficient: 0.7637629255483993 Coefficient of determination (R-squared score, R2 score): 0.5446126584326354
---- ---- ---- class_num = 640 Number of unique elements: 307 [ 0. 40. 80. 120. 160. 200. 240. 280. 320. 360. 400. 440. 480. 520. 560. 600. 640.] test eval: Mean squared error: 3.4444444444444446 Correlation coefficient: 0.4798743430106603 Coefficient of determination (R-squared score, R2 score): 0.1263760457948041 train eval: Mean squared error: 1.6059941520467835 Correlation coefficient: 0.7600503856137294 Coefficient of determination (R-squared score, R2 score): 0.5251608972835786
---- ---- ---- class_num = 656 Number of unique elements: 309 [ 0. 41. 82. 123. 164. 205. 246. 287. 328. 369. 410. 451. 492. 533. 574. 615. 656.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.37497588643165786 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.5467836257309941 Correlation coefficient: 0.7652131149397225 Coefficient of determination (R-squared score, R2 score): 0.5426674823177298
---- ---- ---- class_num = 672 Number of unique elements: 315 [ 0. 42. 84. 126. 168. 210. 252. 294. 336. 378. 420. 462. 504. 546. 588. 630. 672.] test eval: Mean squared error: 3.1666666666666665 Correlation coefficient: 0.5150190255186106 Coefficient of determination (R-squared score, R2 score): 0.19682959048877147 train eval: Mean squared error: 1.560672514619883 Correlation coefficient: 0.7619757686949364 Coefficient of determination (R-squared score, R2 score): 0.5385609994084845
---- ---- ---- class_num = 688 Number of unique elements: 321 [ 0. 43. 86. 129. 172. 215. 258. 301. 344. 387. 430. 473. 516. 559. 602. 645. 688.] test eval: Mean squared error: 4.013888888888889 Correlation coefficient: 0.4005119454382824 Coefficient of determination (R-squared score, R2 score): -0.01805372082782908 train eval: Mean squared error: 1.5482456140350878 Correlation coefficient: 0.7727192950685039 Coefficient of determination (R-squared score, R2 score): 0.5422352209588619
---- ---- ---- class_num = 704 Number of unique elements: 332 [ 0. 44. 88. 132. 176. 220. 264. 308. 352. 396. 440. 484. 528. 572. 616. 660. 704.] test eval: Mean squared error: 3.75 Correlation coefficient: 0.4418255075484136 Coefficient of determination (R-squared score, R2 score): 0.04887714663143994 train eval: Mean squared error: 1.439327485380117 Correlation coefficient: 0.7839238700032121 Coefficient of determination (R-squared score, R2 score): 0.5744386921945226
---- ---- ---- class_num = 720 Number of unique elements: 327 [ 0. 45. 90. 135. 180. 225. 270. 315. 360. 405. 450. 495. 540. 585. 630. 675. 720.] test eval: Mean squared error: 3.486111111111111 Correlation coefficient: 0.4555483337428381 Coefficient of determination (R-squared score, R2 score): 0.11580801409070896 train eval: Mean squared error: 1.5182748538011697 Correlation coefficient: 0.7715449215307933 Coefficient of determination (R-squared score, R2 score): 0.5510965788156543
---- ---- ---- class_num = 736 Number of unique elements: 337 [ 0. 46. 92. 138. 184. 230. 276. 322. 368. 414. 460. 506. 552. 598. 644. 690. 736.] test eval: Mean squared error: 4.208333333333333 Correlation coefficient: 0.41224302218437786 Coefficient of determination (R-squared score, R2 score): -0.06737120211360637 train eval: Mean squared error: 1.662280701754386 Correlation coefficient: 0.7509674113487845 Coefficient of determination (R-squared score, R2 score): 0.5085188349671632
---- ---- ---- class_num = 752 Number of unique elements: 342 [ 0. 47. 94. 141. 188. 235. 282. 329. 376. 423. 470. 517. 564. 611. 658. 705. 752.] test eval: Mean squared error: 3.861111111111111 Correlation coefficient: 0.4226049614507438 Coefficient of determination (R-squared score, R2 score): 0.02069572875385295 train eval: Mean squared error: 1.519736842105263 Correlation coefficient: 0.7694432377079866 Coefficient of determination (R-squared score, R2 score): 0.5506643174567865
---- ---- ---- class_num = 768 Number of unique elements: 355 [ 0. 48. 96. 144. 192. 240. 288. 336. 384. 432. 480. 528. 576. 624. 672. 720. 768.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4702633221611583 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 1.4407894736842106 Correlation coefficient: 0.78251053221998 Coefficient of determination (R-squared score, R2 score): 0.5740064308356547
---- ---- ---- class_num = 784 Number of unique elements: 351 [ 0. 49. 98. 147. 196. 245. 294. 343. 392. 441. 490. 539. 588. 637. 686. 735. 784.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.4910675336428644 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 1.4663742690058479 Correlation coefficient: 0.7824074519633014 Coefficient of determination (R-squared score, R2 score): 0.5664418570554659
---- ---- ---- class_num = 800 Number of unique elements: 355 [ 0. 50. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 600. 650. 700. 750. 800.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.4353159979326409 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.5314327485380117 Correlation coefficient: 0.7676016320869605 Coefficient of determination (R-squared score, R2 score): 0.5472062265858431
---- ---- ---- class_num = 816 Number of unique elements: 365 [ 0. 51. 102. 153. 204. 255. 306. 357. 408. 459. 510. 561. 612. 663. 714. 765. 816.] test eval: Mean squared error: 3.25 Correlation coefficient: 0.5351553225029251 Coefficient of determination (R-squared score, R2 score): 0.17569352708058128 train eval: Mean squared error: 1.4305555555555556 Correlation coefficient: 0.7833717170500211 Coefficient of determination (R-squared score, R2 score): 0.5770322603477303
---- ---- ---- class_num = 832 Number of unique elements: 369 [ 0. 52. 104. 156. 208. 260. 312. 364. 416. 468. 520. 572. 624. 676. 728. 780. 832.] test eval: Mean squared error: 3.1944444444444446 Correlation coefficient: 0.5262219237468545 Coefficient of determination (R-squared score, R2 score): 0.18978423601937477 train eval: Mean squared error: 1.418859649122807 Correlation coefficient: 0.7891367199216424 Coefficient of determination (R-squared score, R2 score): 0.5804903512186737
---- ---- ---- class_num = 848 Number of unique elements: 374 [ 0. 53. 106. 159. 212. 265. 318. 371. 424. 477. 530. 583. 636. 689. 742. 795. 848.] test eval: Mean squared error: 3.2916666666666665 Correlation coefficient: 0.48057246999800624 Coefficient of determination (R-squared score, R2 score): 0.16512549537648613 train eval: Mean squared error: 1.4144736842105263 Correlation coefficient: 0.787556821947226 Coefficient of determination (R-squared score, R2 score): 0.5817871352952775
---- ---- ---- class_num = 864 Number of unique elements: 376 [ 0. 54. 108. 162. 216. 270. 324. 378. 432. 486. 540. 594. 648. 702. 756. 810. 864.] test eval: Mean squared error: 3.9027777777777777 Correlation coefficient: 0.3868950782276027 Coefficient of determination (R-squared score, R2 score): 0.0101276970497578 train eval: Mean squared error: 1.388157894736842 Correlation coefficient: 0.7900191528231353 Coefficient of determination (R-squared score, R2 score): 0.5895678397549002
---- ---- ---- class_num = 880 Number of unique elements: 375 [ 0. 55. 110. 165. 220. 275. 330. 385. 440. 495. 550. 605. 660. 715. 770. 825. 880.] test eval: Mean squared error: 3.4444444444444446 Correlation coefficient: 0.49664932833991754 Coefficient of determination (R-squared score, R2 score): 0.1263760457948041 train eval: Mean squared error: 1.4619883040935673 Correlation coefficient: 0.7809029480746438 Coefficient of determination (R-squared score, R2 score): 0.5677386411320697
---- ---- ---- class_num = 896 Number of unique elements: 388 [ 0. 56. 112. 168. 224. 280. 336. 392. 448. 504. 560. 616. 672. 728. 784. 840. 896.] test eval: Mean squared error: 3.3333333333333335 Correlation coefficient: 0.5034573464200038 Coefficient of determination (R-squared score, R2 score): 0.15455746367239098 train eval: Mean squared error: 1.41593567251462 Correlation coefficient: 0.7847663093290186 Coefficient of determination (R-squared score, R2 score): 0.5813548739364096
---- ---- ---- class_num = 912 Number of unique elements: 393 [ 0. 57. 114. 171. 228. 285. 342. 399. 456. 513. 570. 627. 684. 741. 798. 855. 912.] test eval: Mean squared error: 4.166666666666667 Correlation coefficient: 0.4071858212864697 Coefficient of determination (R-squared score, R2 score): -0.05680317040951133 train eval: Mean squared error: 1.361842105263158 Correlation coefficient: 0.7938235266125524 Coefficient of determination (R-squared score, R2 score): 0.597348544214523
---- ---- ---- class_num = 928 Number of unique elements: 393 [ 0. 58. 116. 174. 232. 290. 348. 406. 464. 522. 580. 638. 696. 754. 812. 870. 928.] test eval: Mean squared error: 3.0277777777777777 Correlation coefficient: 0.5306120337926347 Coefficient of determination (R-squared score, R2 score): 0.23205636283575515 train eval: Mean squared error: 1.3640350877192982 Correlation coefficient: 0.7928116156624162 Coefficient of determination (R-squared score, R2 score): 0.5967001521762211
---- ---- ---- class_num = 944 Number of unique elements: 398 [ 0. 59. 118. 177. 236. 295. 354. 413. 472. 531. 590. 649. 708. 767. 826. 885. 944.] test eval: Mean squared error: 3.2777777777777777 Correlation coefficient: 0.5038584858703183 Coefficient of determination (R-squared score, R2 score): 0.16864817261118448 train eval: Mean squared error: 1.3801169590643274 Correlation coefficient: 0.7907118781047191 Coefficient of determination (R-squared score, R2 score): 0.5919452772286737
---- ---- ---- class_num = 960 Number of unique elements: 398 [ 0. 60. 120. 180. 240. 300. 360. 420. 480. 540. 600. 660. 720. 780. 840. 900. 960.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.4767013049209689 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.3494152046783625 Correlation coefficient: 0.7964253901758411 Coefficient of determination (R-squared score, R2 score): 0.6010227657649003
---- ---- ---- class_num = 976 Number of unique elements: 408 [ 0. 61. 122. 183. 244. 305. 366. 427. 488. 549. 610. 671. 732. 793. 854. 915. 976.] test eval: Mean squared error: 3.986111111111111 Correlation coefficient: 0.46251262770571977 Coefficient of determination (R-squared score, R2 score): -0.011008366358432387 train eval: Mean squared error: 1.404970760233918 Correlation coefficient: 0.7901530589059842 Coefficient of determination (R-squared score, R2 score): 0.5845968341279191
---- ---- ---- class_num = 992 Number of unique elements: 406 [ 0. 62. 124. 186. 248. 310. 372. 434. 496. 558. 620. 682. 744. 806. 868. 930. 992.] test eval: Mean squared error: 4.25 Correlation coefficient: 0.4169227166945107 Coefficient of determination (R-squared score, R2 score): -0.0779392338177014 train eval: Mean squared error: 1.391812865497076 Correlation coefficient: 0.7894680575074436 Coefficient of determination (R-squared score, R2 score): 0.5884871863577303
---- ---- ---- class_num = 1008 Number of unique elements: 414 [ 0. 63. 126. 189. 252. 315. 378. 441. 504. 567. 630. 693. 756. 819. 882. 945. 1008.] test eval: Mean squared error: 4.055555555555555 Correlation coefficient: 0.4171084530480764 Coefficient of determination (R-squared score, R2 score): -0.028621752531924338 train eval: Mean squared error: 1.3874269005847952 Correlation coefficient: 0.7918170168929646 Coefficient of determination (R-squared score, R2 score): 0.5897839704343342
---- ---- ---- class_num = 1024 Number of unique elements: 421 [ 0. 64. 128. 192. 256. 320. 384. 448. 512. 576. 640. 704. 768. 832. 896. 960. 1024.] test eval: Mean squared error: 4.097222222222222 Correlation coefficient: 0.369574849704913 Coefficient of determination (R-squared score, R2 score): -0.039189784236019376 train eval: Mean squared error: 1.331140350877193 Correlation coefficient: 0.7977501577967256 Coefficient of determination (R-squared score, R2 score): 0.6064260327507495
---- ---- ---- class_num = 1040 Number of unique elements: 429 [ 0. 65. 130. 195. 260. 325. 390. 455. 520. 585. 650. 715. 780. 845. 910. 975. 1040.] test eval: Mean squared error: 4.222222222222222 Correlation coefficient: 0.38461444972865816 Coefficient of determination (R-squared score, R2 score): -0.07089387934830471 train eval: Mean squared error: 1.3991228070175439 Correlation coefficient: 0.7902467723105108 Coefficient of determination (R-squared score, R2 score): 0.5863258795633908
---- ---- ---- class_num = 1056 Number of unique elements: 428 [ 0. 66. 132. 198. 264. 330. 396. 462. 528. 594. 660. 726. 792. 858. 924. 990. 1056.] test eval: Mean squared error: 3.3055555555555554 Correlation coefficient: 0.5066201824582414 Coefficient of determination (R-squared score, R2 score): 0.16160281814178779 train eval: Mean squared error: 1.310672514619883 Correlation coefficient: 0.8034802783088595 Coefficient of determination (R-squared score, R2 score): 0.6124776917749005
---- ---- ---- class_num = 1072 Number of unique elements: 435 [ 0. 67. 134. 201. 268. 335. 402. 469. 536. 603. 670. 737. 804. 871. 938. 1005. 1072.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.497773439480096 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.2214912280701755 Correlation coefficient: 0.8173079807102378 Coefficient of determination (R-squared score, R2 score): 0.6388456346658442
---- ---- ---- class_num = 1088 Number of unique elements: 437 [ 0. 68. 136. 204. 272. 340. 408. 476. 544. 612. 680. 748. 816. 884. 952. 1020. 1088.] test eval: Mean squared error: 3.6527777777777777 Correlation coefficient: 0.45987763081270244 Coefficient of determination (R-squared score, R2 score): 0.07353588727432847 train eval: Mean squared error: 1.2982456140350878 Correlation coefficient: 0.8068687064143895 Coefficient of determination (R-squared score, R2 score): 0.616151913325278
---- ---- ---- class_num = 1104 Number of unique elements: 435 [ 0. 69. 138. 207. 276. 345. 414. 483. 552. 621. 690. 759. 828. 897. 966. 1035. 1104.] test eval: Mean squared error: 4.125 Correlation coefficient: 0.3830549835135723 Coefficient of determination (R-squared score, R2 score): -0.04623513870541607 train eval: Mean squared error: 1.280701754385965 Correlation coefficient: 0.8082102913672906 Coefficient of determination (R-squared score, R2 score): 0.6213390496316931
---- ---- ---- class_num = 1120 Number of unique elements: 443 [ 0. 70. 140. 210. 280. 350. 420. 490. 560. 630. 700. 770. 840. 910. 980. 1050. 1120.] test eval: Mean squared error: 4.625 Correlation coefficient: 0.3520103257330956 Coefficient of determination (R-squared score, R2 score): -0.1730515191545574 train eval: Mean squared error: 1.2163742690058479 Correlation coefficient: 0.8173583185109973 Coefficient of determination (R-squared score, R2 score): 0.640358549421882
---- ---- ---- class_num = 1136 Number of unique elements: 446 [ 0. 71. 142. 213. 284. 355. 426. 497. 568. 639. 710. 781. 852. 923. 994. 1065. 1136.] test eval: Mean squared error: 3.763888888888889 Correlation coefficient: 0.452082055121772 Coefficient of determination (R-squared score, R2 score): 0.04535446939674148 train eval: Mean squared error: 1.236842105263158 Correlation coefficient: 0.8162370541258687 Coefficient of determination (R-squared score, R2 score): 0.6343068903977309
---- ---- ---- class_num = 1152 Number of unique elements: 453 [ 0. 72. 144. 216. 288. 360. 432. 504. 576. 648. 720. 792. 864. 936. 1008. 1080. 1152.] test eval: Mean squared error: 3.3055555555555554 Correlation coefficient: 0.5030456830970099 Coefficient of determination (R-squared score, R2 score): 0.16160281814178779 train eval: Mean squared error: 1.253654970760234 Correlation coefficient: 0.8130056879325639 Coefficient of determination (R-squared score, R2 score): 0.6293358847707498
---- ---- ---- class_num = 1168 Number of unique elements: 463 [ 0. 73. 146. 219. 292. 365. 438. 511. 584. 657. 730. 803. 876. 949. 1022. 1095. 1168.] test eval: Mean squared error: 3.763888888888889 Correlation coefficient: 0.41847194394248616 Coefficient of determination (R-squared score, R2 score): 0.04535446939674148 train eval: Mean squared error: 1.159356725146199 Correlation coefficient: 0.8288134090867733 Coefficient of determination (R-squared score, R2 score): 0.6572167424177313
---- ---- ---- class_num = 1184 Number of unique elements: 457 [ 0. 74. 148. 222. 296. 370. 444. 518. 592. 666. 740. 814. 888. 962. 1036. 1110. 1184.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4540681400432646 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 1.2660818713450293 Correlation coefficient: 0.811768015898878 Coefficient of determination (R-squared score, R2 score): 0.6256616632203724
---- ---- ---- class_num = 1200 Number of unique elements: 464 [ 0. 75. 150. 225. 300. 375. 450. 525. 600. 675. 750. 825. 900. 975. 1050. 1125. 1200.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.39485006534468375 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.2002923976608186 Correlation coefficient: 0.8162717842466877 Coefficient of determination (R-squared score, R2 score): 0.6451134243694292
---- ---- ---- class_num = 1216 Number of unique elements: 476 [ 0. 76. 152. 228. 304. 380. 456. 532. 608. 684. 760. 836. 912. 988. 1064. 1140. 1216.] test eval: Mean squared error: 3.9166666666666665 Correlation coefficient: 0.347297234354348 Coefficient of determination (R-squared score, R2 score): 0.006605019815059454 train eval: Mean squared error: 1.0891812865497077 Correlation coefficient: 0.8364000477174324 Coefficient of determination (R-squared score, R2 score): 0.6779652876433919
---- ---- ---- class_num = 1232 Number of unique elements: 480 [ 0. 77. 154. 231. 308. 385. 462. 539. 616. 693. 770. 847. 924. 1001. 1078. 1155. 1232.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.49179006421871096 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.1900584795321638 Correlation coefficient: 0.8222615851130448 Coefficient of determination (R-squared score, R2 score): 0.6481392538815047
---- ---- ---- class_num = 1248 Number of unique elements: 474 [ 0. 78. 156. 234. 312. 390. 468. 546. 624. 702. 780. 858. 936. 1014. 1092. 1170. 1248.] test eval: Mean squared error: 3.1805555555555554 Correlation coefficient: 0.5440613383250746 Coefficient of determination (R-squared score, R2 score): 0.19330691325407312 train eval: Mean squared error: 1.1396198830409356 Correlation coefficient: 0.8289047916554041 Coefficient of determination (R-squared score, R2 score): 0.6630522707624483
---- ---- ---- class_num = 1264 Number of unique elements: 487 [ 0. 79. 158. 237. 316. 395. 474. 553. 632. 711. 790. 869. 948. 1027. 1106. 1185. 1264.] test eval: Mean squared error: 3.611111111111111 Correlation coefficient: 0.44627046270937537 Coefficient of determination (R-squared score, R2 score): 0.08410391897842362 train eval: Mean squared error: 1.0467836257309941 Correlation coefficient: 0.8426554017178337 Coefficient of determination (R-squared score, R2 score): 0.6905008670505619
---- ---- ---- class_num = 1280 Number of unique elements: 488 [ 0. 80. 160. 240. 320. 400. 480. 560. 640. 720. 800. 880. 960. 1040. 1120. 1200. 1280.] test eval: Mean squared error: 3.736111111111111 Correlation coefficient: 0.4095466365789959 Coefficient of determination (R-squared score, R2 score): 0.052399823866138284 train eval: Mean squared error: 1.1396198830409356 Correlation coefficient: 0.8324861876534952 Coefficient of determination (R-squared score, R2 score): 0.6630522707624483
---- ---- ---- class_num = 1296 Number of unique elements: 492 [ 0. 81. 162. 243. 324. 405. 486. 567. 648. 729. 810. 891. 972. 1053. 1134. 1215. 1296.] test eval: Mean squared error: 3.7916666666666665 Correlation coefficient: 0.42597061673103304 Coefficient of determination (R-squared score, R2 score): 0.03830911492734479 train eval: Mean squared error: 1.036549707602339 Correlation coefficient: 0.8427967258110125 Coefficient of determination (R-squared score, R2 score): 0.6935266965626374
---- ---- ---- class_num = 1312 Number of unique elements: 499 [ 0. 82. 164. 246. 328. 410. 492. 574. 656. 738. 820. 902. 984. 1066. 1148. 1230. 1312.] test eval: Mean squared error: 3.4722222222222223 Correlation coefficient: 0.46263440199102385 Coefficient of determination (R-squared score, R2 score): 0.1193306913254073 train eval: Mean squared error: 1.0328947368421053 Correlation coefficient: 0.8440983238529769 Coefficient of determination (R-squared score, R2 score): 0.6946073499598073
---- ---- ---- class_num = 1328 Number of unique elements: 497 [ 0. 83. 166. 249. 332. 415. 498. 581. 664. 747. 830. 913. 996. 1079. 1162. 1245. 1328.] test eval: Mean squared error: 4.180555555555555 Correlation coefficient: 0.3639564680255573 Coefficient of determination (R-squared score, R2 score): -0.060325847644209674 train eval: Mean squared error: 1.0928362573099415 Correlation coefficient: 0.8362356797569905 Coefficient of determination (R-squared score, R2 score): 0.6768846342462221
---- ---- ---- class_num = 1344 Number of unique elements: 501 [ 0. 84. 168. 252. 336. 420. 504. 588. 672. 756. 840. 924. 1008. 1092. 1176. 1260. 1344.] test eval: Mean squared error: 3.5555555555555554 Correlation coefficient: 0.4278885631510579 Coefficient of determination (R-squared score, R2 score): 0.09819462791721711 train eval: Mean squared error: 1.1279239766081872 Correlation coefficient: 0.831651084013057 Coefficient of determination (R-squared score, R2 score): 0.6665103616333918
---- ---- ---- class_num = 1360 Number of unique elements: 503 [ 0. 85. 170. 255. 340. 425. 510. 595. 680. 765. 850. 935. 1020. 1105. 1190. 1275. 1360.] test eval: Mean squared error: 3.4444444444444446 Correlation coefficient: 0.4750872969502953 Coefficient of determination (R-squared score, R2 score): 0.1263760457948041 train eval: Mean squared error: 1.1308479532163742 Correlation coefficient: 0.8315706101253245 Coefficient of determination (R-squared score, R2 score): 0.6656458389156559
---- ---- ---- class_num = 1376 Number of unique elements: 511 [ 0. 86. 172. 258. 344. 430. 516. 602. 688. 774. 860. 946. 1032. 1118. 1204. 1290. 1376.] test eval: Mean squared error: 3.986111111111111 Correlation coefficient: 0.344048389033826 Coefficient of determination (R-squared score, R2 score): -0.011008366358432387 train eval: Mean squared error: 1.0328947368421053 Correlation coefficient: 0.844437469232195 Coefficient of determination (R-squared score, R2 score): 0.6946073499598073
---- ---- ---- class_num = 1392 Number of unique elements: 519 [ 0. 87. 174. 261. 348. 435. 522. 609. 696. 783. 870. 957. 1044. 1131. 1218. 1305. 1392.] test eval: Mean squared error: 4.027777777777778 Correlation coefficient: 0.3611800633782349 Coefficient of determination (R-squared score, R2 score): -0.021576398062527424 train eval: Mean squared error: 1.0453216374269005 Correlation coefficient: 0.8432310597872611 Coefficient of determination (R-squared score, R2 score): 0.6909331284094298
---- ---- ---- class_num = 1408 Number of unique elements: 510 [ 0. 88. 176. 264. 352. 440. 528. 616. 704. 792. 880. 968. 1056. 1144. 1232. 1320. 1408.] test eval: Mean squared error: 4.388888888888889 Correlation coefficient: 0.3307964928843021 Coefficient of determination (R-squared score, R2 score): -0.11316600616468508 train eval: Mean squared error: 1.144736842105263 Correlation coefficient: 0.828920419863793 Coefficient of determination (R-squared score, R2 score): 0.6615393560064107
---- ---- ---- class_num = 1424 Number of unique elements: 523 [ 0. 89. 178. 267. 356. 445. 534. 623. 712. 801. 890. 979. 1068. 1157. 1246. 1335. 1424.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.37666407530779566 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.1038011695906433 Correlation coefficient: 0.833746816153345 Coefficient of determination (R-squared score, R2 score): 0.6736426740547126
---- ---- ---- class_num = 1440 Number of unique elements: 519 [ 0. 90. 180. 270. 360. 450. 540. 630. 720. 810. 900. 990. 1080. 1170. 1260. 1350. 1440.] test eval: Mean squared error: 3.875 Correlation coefficient: 0.39339416969687585 Coefficient of determination (R-squared score, R2 score): 0.017173051519154603 train eval: Mean squared error: 1.162280701754386 Correlation coefficient: 0.8264827454021899 Coefficient of determination (R-squared score, R2 score): 0.6563522196999954
---- ---- ---- class_num = 1456 Number of unique elements: 530 [ 0. 91. 182. 273. 364. 455. 546. 637. 728. 819. 910. 1001. 1092. 1183. 1274. 1365. 1456.] test eval: Mean squared error: 3.4305555555555554 Correlation coefficient: 0.46730321353244414 Coefficient of determination (R-squared score, R2 score): 0.12989872302950245 train eval: Mean squared error: 1.118421052631579 Correlation coefficient: 0.8330034585932155 Coefficient of determination (R-squared score, R2 score): 0.6693200604660333
---- ---- ---- class_num = 1472 Number of unique elements: 525 [ 0. 92. 184. 276. 368. 460. 552. 644. 736. 828. 920. 1012. 1104. 1196. 1288. 1380. 1472.] test eval: Mean squared error: 4.402777777777778 Correlation coefficient: 0.33778786844126274 Coefficient of determination (R-squared score, R2 score): -0.11668868339938343 train eval: Mean squared error: 1.1206140350877194 Correlation coefficient: 0.8328181060974977 Coefficient of determination (R-squared score, R2 score): 0.6686716684277314
---- ---- ---- class_num = 1488 Number of unique elements: 532 [ 0. 93. 186. 279. 372. 465. 558. 651. 744. 837. 930. 1023. 1116. 1209. 1302. 1395. 1488.] test eval: Mean squared error: 3.9027777777777777 Correlation coefficient: 0.3973386098897478 Coefficient of determination (R-squared score, R2 score): 0.0101276970497578 train eval: Mean squared error: 0.9868421052631579 Correlation coefficient: 0.8513763519013561 Coefficient of determination (R-squared score, R2 score): 0.708223582764147
---- ---- ---- class_num = 1504 Number of unique elements: 534 [ 0. 94. 188. 282. 376. 470. 564. 658. 752. 846. 940. 1034. 1128. 1222. 1316. 1410. 1504.] test eval: Mean squared error: 3.7777777777777777 Correlation coefficient: 0.3976083689307804 Coefficient of determination (R-squared score, R2 score): 0.041831792162043135 train eval: Mean squared error: 1.0687134502923976 Correlation coefficient: 0.8414098886090738 Coefficient of determination (R-squared score, R2 score): 0.684016946667543
---- ---- ---- class_num = 1520 Number of unique elements: 538 [ 0. 95. 190. 285. 380. 475. 570. 665. 760. 855. 950. 1045. 1140. 1235. 1330. 1425. 1520.] test eval: Mean squared error: 3.736111111111111 Correlation coefficient: 0.4452256456517434 Coefficient of determination (R-squared score, R2 score): 0.052399823866138284 train eval: Mean squared error: 0.9963450292397661 Correlation coefficient: 0.8493180191035392 Coefficient of determination (R-squared score, R2 score): 0.7054138839315055
---- ---- ---- class_num = 1536 Number of unique elements: 543 [ 0. 96. 192. 288. 384. 480. 576. 672. 768. 864. 960. 1056. 1152. 1248. 1344. 1440. 1536.] test eval: Mean squared error: 4.361111111111111 Correlation coefficient: 0.30649124324470645 Coefficient of determination (R-squared score, R2 score): -0.10612065169528839 train eval: Mean squared error: 0.9254385964912281 Correlation coefficient: 0.8604761215901255 Coefficient of determination (R-squared score, R2 score): 0.7263785598366002
---- ---- ---- class_num = 1552 Number of unique elements: 552 [ 0. 97. 194. 291. 388. 485. 582. 679. 776. 873. 970. 1067. 1164. 1261. 1358. 1455. 1552.] test eval: Mean squared error: 4.916666666666667 Correlation coefficient: 0.3376522863225631 Coefficient of determination (R-squared score, R2 score): -0.24702774108322334 train eval: Mean squared error: 1.1798245614035088 Correlation coefficient: 0.8275789495015552 Coefficient of determination (R-squared score, R2 score): 0.6511650833935803
---- ---- ---- class_num = 1568 Number of unique elements: 546 [ 0. 98. 196. 294. 392. 490. 588. 686. 784. 882. 980. 1078. 1176. 1274. 1372. 1470. 1568.] test eval: Mean squared error: 3.8333333333333335 Correlation coefficient: 0.36276795113160476 Coefficient of determination (R-squared score, R2 score): 0.02774108322324964 train eval: Mean squared error: 1.1308479532163742 Correlation coefficient: 0.8311792384892888 Coefficient of determination (R-squared score, R2 score): 0.6656458389156559
---- ---- ---- class_num = 1584 Number of unique elements: 553 [ 0. 99. 198. 297. 396. 495. 594. 693. 792. 891. 990. 1089. 1188. 1287. 1386. 1485. 1584.] test eval: Mean squared error: 3.75 Correlation coefficient: 0.4037425622438564 Coefficient of determination (R-squared score, R2 score): 0.04887714663143994 train eval: Mean squared error: 1.0504385964912282 Correlation coefficient: 0.8422369224415918 Coefficient of determination (R-squared score, R2 score): 0.6894202136533921
---- ---- ---- class_num = 1600 Number of unique elements: 554 [ 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. 1000. 1100. 1200. 1300. 1400. 1500. 1600.] test eval: Mean squared error: 3.8055555555555554 Correlation coefficient: 0.3784207614719348 Coefficient of determination (R-squared score, R2 score): 0.034786437692646444 train eval: Mean squared error: 1.0789473684210527 Correlation coefficient: 0.8385805409196683 Coefficient of determination (R-squared score, R2 score): 0.6809911171554675
# plot the trend figures of mse, correlation, and r2
# Create a figure and subplots
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
# Plot MSE
ax1.plot(class_num_array, mse_test_list, label='MSE (Test)')
ax1.plot(class_num_array, mse_train_list, label='MSE (Train)')
ax1.set_ylabel('MSE')
ax1.set_xlabel('Original Class Number')
ax1.set_title(f'MSE Curve (reduced class num is {reduced_class_num})')
ax1.legend()
# Plot Correlation
ax2.plot(class_num_array, correlation_test_list, label='Correlation (Test)')
ax2.plot(class_num_array, correlation_train_list, label='Correlation (Train)')
ax2.set_ylabel('Correlation')
ax2.set_xlabel('Original Class Number')
ax2.set_title(f'Correlation Curve (reduced class num is {reduced_class_num})')
ax2.legend()
# Plot R-squared
ax3.plot(class_num_array, r_squared_test_list, label='R-squared (Test)')
ax3.plot(class_num_array, r_squared_train_list, label='R-squared (Train)')
ax3.set_ylabel('R-squared')
ax3.set_xlabel('Original Class Number')
ax3.set_title(f'R-squared Curve (reduced class num is {reduced_class_num})')
ax3.legend()
# Increase the vertical spacing between subplots
plt.subplots_adjust(hspace=0.5)
# Adjust tick, label, title, and legend font sizes
plt.rcParams.update({'font.size': 12})
ax1.tick_params(labelsize=10)
ax2.tick_params(labelsize=10)
ax3.tick_params(labelsize=10)
# Save the figure
plt.savefig(f'mse_correlation_r2_trend_curve_reduced_eval_reduced_class_num_{reduced_class_num}.png', bbox_inches='tight')
# Show the figure
plt.show()
# Convert r_squared_test_list to a NumPy array
r_squared_test_array = np.array(r_squared_test_list)
# Find the index of the maximum value
max_index = np.argmax(r_squared_test_array)
# Get the corresponding class_num value
max_class_num = class_num_array[max_index]
# Print the index and corresponding class_num
print("Max Index:", max_index)
print("Max Original Class Num:", max_class_num)
Max Index: 29 Max Original Class Num: 480
# batch download the plotted figures
# uncomment the code below to download figures if needed
'''
import glob
folder_path = '.'
file_prefix = 'Comparison of Sorted Predictions and Sorted Ground Truth (Logistic Linear Regression Reduced Evaluation'
# Use glob to find all files with the given prefix in the folder
matching_files = glob.glob(f"{folder_path}/{file_prefix}*")
# print(matching_files)
# # Print the matching file names
# for file_path in matching_files:
# print(file_path)
import zipfile
zip_filename = 'files.zip'
with zipfile.ZipFile(zip_filename, 'w') as zipf:
# Add files to the zip file
for file_path in matching_files:
zipf.write(file_path)
from google.colab import files
files.download(zip_filename)
'''
balanced weights don't improve the fitting, but make it worse.
# independent data
x = group_satcked_green
class_num = 48
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 25) y_train shape: (1368,) x_test shape: (72, 25) y_test shape: (72,) Unique elements: [ 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 42 47] Number of unique elements: 40
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, class_weight='balanced', multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
# Print the predicted class labels
print(y_pred, y_test)
print(y_pred.shape, y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(40,) (40, 25) [ 5 27 22 22 9 29 11 25 22 29 5 23 5 10 6 8 8 29 22 10 26 36 11 26 12 16 22 26 31 34 10 9 29 7 24 6 32 13 20 10 9 34 8 21 14 7 29 28 19 11 9 20 8 14 10 23 20 3 28 3 12 10 14 11 19 3 13 20 20 12 20 24] [19 13 25 35 13 21 10 18 17 28 15 18 7 16 10 8 10 12 25 29 14 21 12 16 11 16 13 14 9 18 15 13 18 12 11 10 30 16 14 12 12 12 30 12 12 13 17 28 11 17 9 15 11 15 16 22 18 10 17 7 18 11 12 9 15 13 8 22 17 11 16 16] (72,) (72,)
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_test, y_pred)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_test, y_pred, 'Logistic Linear Regression balanced weights, Test Set')
Accuracy: 0.05555555555555555 Confusion Matrix: [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] Correlation coefficient: 0.4046314021861102
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
cm = confusion_matrix(y_train, y_pred_)
print("Confusion Matrix:")
print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression balanced weights, Train Set')
Accuracy: 0.15862573099415206 Confusion Matrix: [[2 0 0 ... 0 0 0] [0 1 0 ... 0 0 0] [0 0 2 ... 0 0 0] ... [0 0 0 ... 1 0 0] [0 0 0 ... 0 1 0] [0 0 0 ... 0 0 2]] Correlation coefficient: 0.5813149974591648
